Question

Упростите выражение
(2/x^2-4+1/2x-x^2):1/x^2+4x+4

Answer 1

$( frac{2}{x^2-4} + frac{1}{2x-x^2} ) : frac{1}{x^2+4x+4} = ( frac{2}{x^2-2^2} + frac{1}{-x(x-2)} ) : frac{1}{x^2+2*2x+2^2}= \ \ = (frac{2}{(x-2)(x+2)} + frac{1}{-x(x-2)} ) * frac{(x+2)^2}{1} = frac{2*(-x) +1(x+2)}{-x(x-2)(x+2)} * frac{(x+2)^2}{1} = \ \ = frac{-2x+x+2}{-x(x-2)(x+2)} * frac{(x+2)^2}{1} = frac{(2-x)(x+2)}{-x(x-2)} = \ \ = frac{-(x-2)(x+2)}{-x(x-2)} = frac{-(x+2)}{-x} = frac{x+2}{x} = 1 + frac{2}{x}$